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Holography and Coherent Optics
Holography and Coherent Optics L.M.Soroko Joint Institute for Nuclear Research Dubna, USSR
Translated from Russian by Albin Tybulewicz Editor, Soviet Journal of Quantum Electronics
With a Foreword by George W. Stroke Translation Editor State University of New York at Stony Brook
PLENUM. PRESS· NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Soroko, Lev Markovich. Holography and coherent optics.
Translation of Osnovy golograiJi i kogerentnoloptiki. Bibliography: p. Includes index. 1. Holography. 2. Infonnation theory in optics. 3. Coherence (Optics) I. Title.
QC449.S6713 535'.4 784479
ISBN-13: 978-1-4684-3422-4 e-ISBN-13: 978-1-4684-3420-0 DOT: 10.1007/978-1-4684-3420-0
The original Russian text, published by Nauka Press in Moscow in 1971, has been corrected by the author for the present edition. This translation is published under an agreement with the Copyright Agency of the USSR (V AAP).
OCHOBbI fOJIOfPAIDHH H KOfEPEHTHOH OnTHKH JI.M.COPORO
OSNOVY GOLOGRAFII I KOGERENTNOI OPTIKl L. M. Soroko
© 1980 Plenum Press, New York Softcover reprint of the hardcover I st edition 1980
A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011
All righ ts reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any fonn or by any means, electronic, mechanical, photocopying, microfllming, recording, or otherwise, without written pennission from the Publisher
Foreword
Now that holography has matured (wIth Dennis Gabor having received the Nobel Prize In 1971) and that coherent optics has proved to be even more powerful than originally imagined, in opening the new field of "optical computing," it is particularlyappropriate to make available to English-speaking readers the translation of a uniquely outstanding text which presents the general and permanent foundations of the field.
L. M. Soroko's book has proved its usefulness, since It appeared in Russian In 1971, following the basic pattern set in the world's first monograph In the field, "An Introduction to Coherent Optics and Holography," written by G. w. Stroke in 1966, and since also available in Its second US edition (1969) from Academic Press, following the publication of its Russian edition by Mlr In 1967.
To further enhance the usefulness of L. M. Soroko's book, and to assure that Its fundamental nature be completely updated, the Translation Editor, In agreement with the author, felt that this could best be assured by including an "updating appendix" In the form of three recent papers In the general field of "opto-dlgltal holographic Image processing and 3-D reconstructions," especially -also since their bibliographies Include numerous further references to a great many authors and workers throughout the world. In addition, the reader's attention Is drawn to two books, also recently pubUshed by Plenum Press, under ihe title "Optical Information Processing," the first In 1976 (edited by Yu. E. Nesterikhln, G. w. Stroke, and w. E. Kock), and the second In 1977 (edited by E. S. Barrekette, G. w. Stroke, Yu. E. Nesterlkhln, and W. E. Kock).
v
vi FOREWORD
These books present the complete set of papers from two US-USSR science cooperation seminars. organized and co-chaired by Academician Yu. E. Nesterikhin. for the USSR. and Prof. G. w. Stroke. for the USA. and held respectively in June 1975 at the National Academy of Sciences in Washington. D. C. under sponsorship from the National Science Foundation. and in July 1976 in the Soviet science city of Akademgorodok (Novosibirsk). under sponsorship of the Academy of Sciences of the USSR. Among the US participants in these seminars. there were W. E. Kook. David Casasent. J. W. Goodman. A. Korpel. Rolf Landauer. Brian J. Thompson. A. Vander Lugt. E. S. Barrekette. W. K. Pratt. M. P. Zampino. H. Kogelnik. S. H. Lee. A. Kozma. and J. C. Urbach. in addition to G. W. Stroke. Papers from all these participants. and a counterpart series of papers from the USSR participants. are included in the two "Optical Information Processing· volumes. In addition. seminar reports have also appeared in Applied Optics. which. in the recent years. together with the IEEE Proceedings. have been perhaps most representative of the progress and ramifications of the work in th~ field.
Stony Brook. N. Y .• 18 January 1978
George W. Stroke Translation Editor
Preface
This monograph on the fundamentals of holography and coherent optics is a considerably revised and expanded version of a course of lectures first presented by the author to senior undergraduates at the Moscow Physicotechnical Institute and to participants of a continuous seminar on holography in 1966-67.
The science of holography was founded about 30 years ago but it has grown only since the appearance of lasers in pliysicallaboratories. It is now rapidly and widely applied in seemingly most unlikely branches of science and technology. This process is accompanied by the continuous growth of the number of specialists who are developing optical systems suitable for their applications. These systems are based on the modern coherent optics and holography. This wide range of specialists needs a modern and comprehensive treatment of the theory and physical principles underlying holography. 'The present book is intended to fill this need, and the first step in this direction is a discussion of the theory of holography. Many of the subjects discussed in the present monograph represent the essence or development of numerous discussions in which the author has participated.
During the writing of this book the first and only monograph on holography in the world literature was G. W. Stroke'S "An Introduction to Coherent Optics and Holography," published by Academic Press in 1966. The Russian translation of this book was published by Mir in 1967. Stroke's book is used widely throughout the world and a greatly enlarged second edition has been published in 1969.
vii
vUi PREFACE
The reviews on holography published in various journals have also been necessarily brief. Therefore, even if they were collected together, they would not provide a systematic treatment of the subject which is needed during a period of rapid spread of holography to various branches of science and technology.
The intention of the present author has been to present the fundamentals of holography in a sufficiently comprehensive form and from the same point of view. The present monograph is effectively an attempt to provide such a systematic treatment on the basis of physical optics, statistical radiophysics, and information theory, which are leading branches of modern science.
Holography is a relatively new subject and, therefore, the monograph begins with an introductory and descriptive chapter in which the physical basis of holography is presented in a clear but somewhat simplified manner. In spite of that, all the aspects of holography are introduced rigorously and this applies also to the concept of coherence of light which is of basic importance in holography.
The second chapter introduces the concept of an optical signal and deals in detail with the properties of integral linear transformations which can be applied to an optical signal. These transformations are of direct relevance to holography, Fourier spectroscopy, synthesis (computer generation) of holograms, and preparation of two-dimensional translators and filters for coherent optical systems.
The discussion is illustrated by several systems in which incoherent illumination is used. A detailed discussion of correlators and complex two-dimensional filters is deferred to the seventh chapter.
The general properties of integral transformations with Fourier-type kernels are formulated at the end of the second chapter. These transformations have the property of invertlbility and they can be used to build multistage optical information processing systems in which there are hardly any losses of any aspects of information.
The third chapter deals with the main properties of a random optical signal. 'The material in this chapter is used later in dealing with the coherence of light (in the fourth chapter), the fundamentals of holography (in the sixth chapter), and the optical in-
PREFACE
formation processing method and filtering of optical signals (in the seventh chapter).
The fourth chapter is devoted to the classical (nonquantum) theory of coherence. '!be latest experiments on the coherence of light are described and methods for measuring coherence are discussed. The theory of coherence of light is basic to holography.
The fifth chapter is devoted to the information structure of an optical signal, particularly those information invariants which determine the resolution in optics and holography, the information capacity of the message being transmitted, and the influence of the degree of coherence of Ught on the amount of information which can be transmitted without distortion by a partially coherent light beam.
The sixth chapter deals with the following top ics: the principle of holography as a method for complete recording of light waves; the relationship between an object and the optical signal recorded in a hologram of this object; the classification of holograms and the resolution requirements which must be satisfied by recording materials; the various holographic systems, including those employing coherent illumination and spatially coherent illumination, ,achromatic systems. volume and stroboscopic holograms, and synthesized (computer-generated) holograms. Generalized holography is discussed at the end of the chapter and possible ways of bull ding a holographic x-ray microscope are discussed.
The seventh chapter· deals with optical information processing methods, primarily those based on the holographic principle. Coherent methods for image (pattern) recognition, spatial differentiation of optical signals, and methods for preparing two-dimensional translators are discussed.
The monograph deliberately restricts itself to the fundamental theory of holography, and therefore does not deal with recording materials or with the theory of aberrations in holography (in particular. the aberration theory of the holographic microscope). Applications of holography in various branches of science and technology are also not considered, in order to maintain the size of the volume within customary limits.
In the writing of the present monograph it has been necessary to partly rephrase some of the nomenclature used in those disci-
x PREFACE
plines which make essential contributions to holography. This rephrasing and the very compact notation used in the basic relationships simplify the amalgamation of these disciplines and make it possible to develop a new language suitable for the description of the fundamental prinCiples of holography and radio-frequency optics which are essentially interdisciplinary subjects and are among the youngest branches of modern science.
The monograph is written for a wide range of researchers, including physiCiSts, radiophysicists, biophysicists, engineers, and mathematicians working in image recognition and other branches of cybernetics. The monograph can also be used as a textbook for undergraduate and graduate students.
Naturally, it has been difficult to avoid shortcomings in writing the first monograph on a young branch of applied physics such as holography. The author will be very grateful to the readers who will respond to his request for critical comments and suggestions.
The author is deeply grateful to Professor Ya. A. Smorodinskii,who has stimulated the author's interest in holography, and to the Corresponding Member of the USSR Academy of Sciences V. P. Dzelepov for his constant encouragement of the author's research in holography. The author is also grateful to Academician B. M. Pontekorvo (pontecorvo), Corresponding Member of the USSR Academy of Sciences I. I. Gurevich, Doctor of Physicomathe-mati cal Sciences G. I. Kopylov, Candidate of Physicomathematical Sciences A. F. Pisarev, and Engineer I. P. Nalimov for interesting discussions of holography, and to Professors S. L. Mandel'shtam and G. V. Skrotskii, who have responded in a lively manner to the progress in optics and quantum electronics, have introduced important modifications into senior undergraduate course~, and have greatly encouraged the author.
The author is particularly grateful to V. M. Soroko without whose help in many matters this book would not have been written.
Thanks are also due to Professor G. W. Stroke of the State UniverSity of New York at Stony Brook for scientific contacts which have helped the author to gain a fuller understanding of the latest achievements in holography.
L. Soroko
.Dubna, 1969
Contents
Chapter 1 Introduction
§ 1.1
§1.2
§1.3 §1.4 § 1.5 §1.6 §1.7
Chapter 2
Principle of Holography. Interference of Light ..............••.........•
Three-Dimensional Nature of an Image. Parallax ......•................•.
Plane Hologram ..••............•...•. Diffraction of Light in a Plane Hologram . . . . • . Coherence of Light • . . . . . . . . . . . . . . • . . . . Light Sources for Holography ..•••.. . . . . • . History of Holography . . . • . . . . . . . . . . . . . .
1
3
11 13 16 20 26 30
Optical Signal and Its Transformations. ••• 43
§2.1 §2.2 §2.3 §2.4
§ 2.5
§ 2.6 §2.7 §2.8 § 2.9
§2.10
Complex Signal in Optics .••••....••••... Fourier Transformation • • . . . • . . . • • • • • • . . Properties of Fourier Transformation ••..... Typical Fourier Transformations and
Standard Notation for Commonly Occurring
43 48 49
Functions. • • • • . . . . . . . . . . . . . . . . . . • . 57 Optical Systems Performing Fourier
Transformation. . . • • . . . . . . • . . . . . . . • . Convolution and Its Properties .........•.•. Correlation and Its Properties. • • • . • . . ..... Convolution and Correlation in a Plane ...•... Optical System for Convolution and Cross-
Correlation Operations .•..•.•..••...•• Scalar Products of Functions. • . • . • • . . . . . . •
xl
65 68 72 73
74 78
xli
§2.11 §2.12 §2.13
§2.14 §2.15
§ 2.16 §2.17
§2.18 §2.19 § 2.20 §2.21 §2.22 §2.23
§2.24
§ 2.25 § 2.26 §2.27
§2.28 §2.29 §2.30 §2.31 §2.32
Chapter 3 Random
§3.1 §3.2 § 3.3 § 3.4
CONTENTS
Generalized Functions or Distributions . • • . . • • 81 Examples of Generalized Functions ...• . . . . . 84 Fourier Transformation of Generalized
Functions. • • . . . . . . . . . . . • • . • . • • • . . . 91 Convolution of Generalized Functions. .• • . . . •• 100 Fourier Transformation and Convolution
of Functions in Multidimensional Spaces . . .. 107 Delta Functions in a Plane ••••.. . . • . • • . •. 111 Fourier Transformation of Radial Functions
Defined in a Plane . . . . . . . • • . . . . . • . . •• 115 Hankel Transformation. . . . . . . . . . . . . . . . .. 119 Truncated Fourier Transformation. • • • . . . . .. 121 Hilbert Transformation ... . . . . . . • . • . . . •. 128 Linear Filter . . . . . . . . . . . . . . • . • • . . . • •• 131 Linear Two-Dimensional Filter. . • • . . . . . . .. 137 Dispersion Relationships and Causality
Principle • • . . . . . • • • . • . . . . . • .. • . . • .• 143 Relationship Between Fourier, Hilbert, and
Hankel Transformations • . . • • . • • . . . . . •• 148 Modulation of a Signal ...•. . . . . . • . . . . . •• 154 Fresnel Transformation. • • . . . . • . . . . . • • .• 167 Relationship Between Fresnel and Fourier
Transformations • • • • • . • • • • • • • • . • • • •• 172 Fresnel Sandwich . • • • • . . • • . • • . • • • • • • . . Bickel- Bowman System ..•...•.•••..••.• Auxiliary Parameter in Fresnel Transformation. Dirac and Sampling Transformations ••....•. Comparison of Integral Transformations Used
in OptiCS •........................
Signal •••••••••••••••••••••••••••
Random Function and Random Signal ••••••••• Stationary Random Signal • • • • • • • • • • • • • • • • Correlation Functions •••••••••••••••••• Fourier Transformation of Cross-Correlation
175 177 182 183
184
193
193 196 198
Functions • • • • • • • • • • . • • • • • • • . . • . • • 206 § 3.5 Average Power. • • • • • • • • • • • • • • • • • • • • • • 207 § 3.6 Energy Spectrum. and lts Physical Meaning •••• 216
13.7 13.8
13.9 13.10 13.11
Chapter 4
CONTENTS xW
RBDdom Noise BDd Interference. • • • • • • • • • •• 219 Correlative Methods for Suppression of
Noise and Interference. • • • • • • • • • • • • • • • 221 Detection of a Signal of Known Waveform. • • • • • 223 Indeterminacy Function ••••••••••••••••• 226 Reconstruction of a Function From Its
Autocorrelation •••••••••••••••••••• 233
Coherence of Light....................... 239
14.1 Mutual Coherence Function. • • • • • • • • • • • • •• 239 14.2 Properties of an Analytic Signal and of
Mutual Coherence Function • • • • • • • • • • • • • 247 §4.3 Emission of Light by Atoms •••••••••••••• 249 §4.4 Temporal and Spatial Coherence ••••••••••• 256 14.5 Temporal Coherence • • • • • • • • • • • • • • • • • • • 258 §4.6 Interference of Waves of Different
Frequencies • • • • • • • • • • • • • • • • • • • • • • • 261 14.7 Generalization of Mutual Coherence Function
to Interference of Light of Different Frequencies • • • • • • • • • • • • • • • • • • • • • •• 270
§ 4.8 Transverse and Longitudinal Spatial
§4.9
14.10
14.11
14.12
14.13
14.14
14.15
14.16
Coherence • • • • • • • • • • • • • • • • • • • • • • • 274 Incoherent Extended Source Generating
Spatially Coherent Light • • • • • • • • • • • • • •• 282 ReJationship Between Coherence and
Diffraction of Light • • • • • • • • • • • • • • • • •• 284 Coherence Determination and Measurement
Methods. • • • • • • • • • • • • • • • • • • • • • • • • • 300 Relationship Between Coherence and
Emission Spectrum • • • • • • • • • • • • • • • • • • 316 Wave Equation of Mutual Coherence
Function ••••••••••••••••••••••••• 318 Integral Representation of Mutual Coherence
Function •••••••••••••••••••••.••• 320 Measurement of Coherence of a Laser
Beam. ••••••••••••••••••••••••••• 324 Coherence and Diffusing Screens •••• • • • • • • • 328
xiv CONTENTS
Chapter 5 Information Structure of Optical
Signals •...•..........•.••..•..•.••.•. 335
§ 5.1 Introduction • • • • • • • • • • • • • • • • • • • • • • • • • 335 § 5.2 Indeterminacy Principle • • • • • • • • • • • • • • • • • 336 § 5.3 Classical Representation of a Signal in
Information Theory • • • • • • • • • • • • • • • • • • 338 § 5.4 Elementary Signal. • • • • • • • • • • • • • • • • • • • • 342 § 5.5 Determinate Function With a Bounded
Spectrum . • • . • • . . • • . • • . • • • . . • . • • .• 344 § 5.6 Properties of Sampling Function ••••••••••• 350 §5.7 Determinate Function of Finite Duration. • • • •• 351 § 5.8 One-Dimensional Functions With
Finite Spectra. • • • • • • • • • • • • • • • • • • • • • 353 § 5.9 Two-Dimensional Functions With
§ 5.10 §5.11 § 5.12 §5.13 § 5.14
Chapter 6
Finite Spectra. • • • • • • • • • • • • • • • • • • • • • 362 Sampling Theorem in Optics • • • • • • • • • • • • • • 366 lliumination Matrix • • • • • • • • • • • • • • • • • • • • 371 Intensity Matrix •••••••••••••••••••••• 380 Image and Detector Matrices. • • • • • • • • • • • •• 383 Temporal Sampling Points ••••••••••••••• 392
Holography ..•....•.••.• 0......... .. .. ... 395
§ 6.1 Introduction • • • • • • • • • • • • • • • • • • • • • • • •• 395 § 6.2 Basic Holographic System. • • • • • • • • • • • • • •• 399 § 6.3 Development of Photographic Emulsions • • • • •• 404 § 6.4 Relationship Between an Object and a Light
Wave Reaching Entrance Pupil. • • • • • • • • •• 410 § 6.5 Holograms of Very Simple Objects • • • • • • • • •• 417 § 6.6 Holographic Microscope. • • • • • • • • • • • • • • • • 421 § 6.7 Relation Between an Object and a Light
Wave Reaching Entrance Pupil for Arbitrary lliumination • • • • • • • • • • • • • • •• 424
§ 6.8 Theory of Most General Holographic System 428 § 6.9 Alternative Representations of Spherical
§ 6.10 §6.11
Fresnel Transform and Its Fourier Transform. • . . • • • • • • • • • . • • • • • • . • • •. 434
Rigorous Classification of Holograms. • • • • • • • 440 Most Typical Systems for Obtaining Different
Types of Hologram •••••••••••••••••• 447
§6.12 §6.13 §6.14
§6.15
§ 6.16 § 6.17
§ 6.18
§ 6.19 § 6.20 § 6.21
§ 6.22 § 6.23 § 6.24 § 6.25
§6.26 § 6.27 §6.28 § 6.29
§6.30
Chapter 7
CONTENTS xv
Absorption and Relief-Phase Hologr;oams • • • • •• 452 Amplitude Synthesis of Images. • • • • • • • • • • •• 457 Correlative Compensation of Extended
Reference Source Effects • • • • • • • • • • • • •• 459 Theory of Correlative Compensation of Extended
Source Effects ••••••••••••••••••••• 462 Holograms of Phase Objects • • • • • • • • • • • • •• 465 Information Capacity of a Photographic
Emulsion and Its Use in Holography. • • • • •• 480 Some Features of Amplitude Synthesis of
Images by Holography •••••••••••••••• 485 Synthesized Holograms. • • • • • • • • • • • • • • • • • 489 Coherence in Holography •••••••••••••••• 505 Intensity Holograms Obtained Under Incoherent
Illumination Conditions. • • • • • •.• • • • • • • •• 519 Holograms Formed with a Fresnel Zone Plate. • 532 Achromatic Holography ••••••••••••••••• 535 Volume Holograms •••••••••••••••••••• 545 Vector Field Holograms of Two Polarization
States • • • • • • • • • • • • • • • • • • • • • • • • • •• 560 Ghost Images • • • • • • • • • • • • • • • • • • • • • • •• 562 Polychromatic Images • • • • • • • • • • • • • • • • • • 563 Aberrations in Holography ••••••••••••••• 567 Generalized Hologram and Principle
of a Reference Object. • • • • • • • • • • • • • • • • 572 Stroboscopic Holograms. • • • • • • • • • • • • • • •• 575
Optical Information Processing Methods.... 579
§ 7.1 Increasing Importance of Optics in Computing Technology • • • • • • • • • • • • • • • • 579
§ 7.2 Fourier Transformation in a Coherent Optical System • • • • • • • • • • • • • • • • • • • • • 580
~ 7.3 Linear Optical Filter • • • • • • • • • • • • • • • • • • • 585 § 7.4 Principle of Spatial Filtering of Images ••••••• 587 § 7.5 Optical Correlator ••••••••••••••••••••• 587 § 7.6 Convolution and Correlation in Coherent
Optical Systems . . . . . . . . . . . . . . . . . . . . 593 § 7.7 Image Recognition • • • • • • • • • • • • • • • • • • • • • 596 § 7.8 Binary Matched Filter • • • • • • • • • • • • • • • • •• 599
xvi
§ 7.9 §7.10 §7.11 § 7.12 § 7.13 § 7.14 § 7.15 § 7.16 § 7.17 § 7.18
§ 7.19 § 7.20
§ 7.21 ~ 7.22 § 7.23
§ 7.24 § 7.25 § 7.26 § 7.27
§7.28
§ 7.29 §7.30 §7.31 §7.32
CONTENTS
Main Components of a Coherent Optical System. 601 Generalized Fresnel Function • • • • • • • • • • • • • 604 Optical stage •••••••••••••••••••••••• 606 Im.aging Condition • • • • • • • • • • • • • • • • • • • • • 608 Condition for Obtaining a Fourier Transform. • • 610 Change of Scale in a Fourier Transform • • • • • • 612 Multistage Optical Systems • • • • • • • • • • • • • • • 614 Multichannel Systems. • • • • • • • • • • • • • • • • • • 616 Spatial Invariance of Linear Optical Filter •••• 618 Suppression of Noise by Spatial Differentiation
of Optical Signals ••••••••••••••••••• 622 Permissible Displacements of a Filter. • • • • • • 627 Some Optical Systems Used in Preparation
of Matched Filters. • • • • • • • • • • • • • • • • • • 635 File of Matched Filters. • • • • • • • • • • • • • • • • • 639 Capacity of Matched-Filter File. . . . • . . . . . .• 642 Incoherent Optical Information Processing
Systems. . • . • . . • • • . • . . . . • . . . . . • • .. 650 Two-Dimensional Translator. • • • • • • • • • • • • • 658 Temporal Holographic Filter. • • • • • • • • • • • • • 662 Correlative Comparison of Two Signals. • • • • • • 666 Redistribution of Information Degrees of
Freedom . • • • • • • • • • • • • • • • • • • • • • • • • 671 Operation of a Coherent Side-Looking
Radar Station • • • • • • • • • • • • • • • • • • • • • • 683 Theory of Coherent Side-Looking Radar •••••• 687 Analysis of Data in a Coherent Radar Frame. • • 695 A Posteriori Image Processing Apodization 699 Removal of Spherical Aberration of Lenses • • • • 702
A p pen d i x . • • • • . . . . . . . . . . . . . . . . . • • . . . . . • . . 703
Optical Computing, by George W. Stroke. . . . . . . . . • • • • 705 Retrieval of Good Images from ACCidentally
Blurred Photographs, by George W. stroke, Maurice Halioua, Venugopal Srinivasan, and Morimasa Shinoda. • • . . . • • • • • • . • • • . . • . . • . 749
Image Improvement and Three-Dimensional Reconstruction Using Holographic Image Processing by George W. Stroke, Maurice Halioua, Friedrich Thon, and Dieter H. Willasch • • • • • • • • • . . . • . • • • • 755
Holography and Coherent Optics